Beyond Persistent Homology: More Discriminative Persistent Invariants

Persistent homology has been an important tool in topological and geometrical data analysis to study the shape of data. However, its ability to differentiate between various datasets is limited. To expand and enhance the toolkit, we study persistent invariants that can be more discriminative than persistent homology. In this talk, we discuss persistent invariants that capture ring-theoretic information about the evolution of the cohomology structure across a filtration.